Core-halo mass relation of ultralight axion dark matter from merger history

In the context of structure formation with ultralight axion dark matter, we offer an alternative explanation for the mass relation of solitonic cores and their host halos observed in numerical simulations. Our argument is based entirely on the mass gain that occurs during major mergers of binary cores and largely independent of the initial core-halo mass relation assigned to hosts that have just collapsed. We find a relation between the halo mass $M_h$ and corresponding core mass $M_c$, $M_c\propto M_h^{2\beta -1}$, where ($1-\beta$) is the core mass loss fraction. Following the evolution of core masses in stochastic merger trees, we find empirical evidence for our model. Our results are useful for statistically modeling the effects of dark matter cores on the properties of galaxies and their substructures in axion dark matter cosmologies.

Figure 1

The core mass with respect to the halo mass at $z=0$ for different initial core-halo mass relation: $n=1/3$ (left), $n=1$ (center), and $n=2$ (right). The dashed line shows the core-halo mass relation from [11], $n=1/3$, at $z=0$. The solid lines show the linear and square relations for comparison.

Figure 2

Left: the halo mass with respect to the number of first-formed halos. The solid line corresponds to Eq. (1). Center: the number of minor mergers with respect to the number of major mergers [solid line given by Eq. (3)]. Right: the halo mass with respect to the number of major mergers [solid line given by Eq. (4)].

Figure 3

The core-halo mass relation at $z=0$ for different $\beta$ compared with predictions of different models. The three lines are matched at $M_h=10^{12}{M}_{\odot }$.